Games can help. An application of bargaining theory to water conflicts in Italy

Carlo Carraro, Alessandra Sgobbi

11 January 2008



Water is fundamental for life and a major concern in many areas of national and international policy. Conflicts about water are behind several political, economic and military disputes around the world. For this reason, national and international negotiated decision-making procedures have been implemented to share and cooperatively manage water resources. There are many examples of international cooperative efforts to manage shared water resources, such as the Aral, Baltic, and Caspian Seas (Conca and Dabelko 2002). Decisions negotiated by interested parties can result in easier implementation, less litigation and improved stability of agreements, and management choices better adapted to local conditions.

But what factors determine the outcome of negotiations? How should parties share the gains from potential cooperation? Can the identification of factors influencing the likelihood of agreement – and/or its type – together with the understanding of their interactions at the theoretical level help reach an agreement in practice?

Most empirical analyses of negotiations adopt an ad hoc approach without exploring the underpinning theories, or attempting to develop a unified formal theory of negotiation (Yoffe et al., 2004). Furthermore, the literature neglects failed negotiation attempts, thus offering an incomplete exploration of negotiations strategies and outcomes (Dinar and Alemu, 2000, p. 333). As a result, we are still far from a broad understanding of agreement determination and how bargaining processes can be shaped to improve negotiation outcomes. Hence, there is rising demand for negotiation theories and applied simulation models that aid decision makers as a ‘negotiation support tool’.

The basic negotiation process typically involves agents making offers and counter-offers over the terms of the agreement. The seminal paper in non-cooperative bargaining theory formally modelling this process is the work of Rubinstein, published in 1982 (Rubinstein, 1982). Despite recent developments in bargaining theory, however, applications of theoretical models to existing negotiation problems remain scanty.1 The characteristics intrinsic to water resources, as well as recent policy trends of participatory planning, make the approach particularly well suited for this area.

Simulating negotiations

We developed a numerical model to simulate multiple water users negotiating how to share water resources in the winter and summer periods (Sgobbi and Carraro, 2007). Through simulation exercises, we explored the impacts of various factors on agents’ strategies and the resulting agreements. Uncertainty over water availability was also included in the model. Uncertainty is a key aspect of water management that will become more critical as climate change impacts the water cycle and water demand.
Computer simulation tools offer valuable support for investigators unable to observe the position of negotiators with a high degree of precision. Our simulations explored a wide variety of preferences and policies and identified robust and stylized facts that may help negotiators formulate strategies.

Application to Piave River Basin

Our model was tested through an application to the water-sharing problem of the Piave River Basin. The Piave River Basin is among the five most important rivers in Italy, and plays a crucial role in the socio-economic development of the Veneto region. The main water users in the Piave River Basin are: the two major Land Reclamation Boards in the low part of the river, who represent farmers and require water, especially in the summer, for agricultural production; ENEL, the electricity company, which manages the main reservoirs in the Piave River System; the Province of Belluno, which has traditionally suffered from the management of the Piave’s artificial lakes that eliminates the reservoirs’ value in terms of landscape and tourist services; and a constitutional agent, representing the interests of the lower land riverside municipalities, who defends the environmental functionality of the river’s closing reach.

The five water users negotiate, through offer and counteroffer, how to share water resources in the winter and summer. Different water users have different bargaining powers, determined by legislation, or by the strength of the relationship linking them to water managers and authorities. We approximated bargaining power with access probabilities, determining the order in which water users are called upon to make an offer. The River Basin Authority does not take part in the game, but rather sets the rule.

Formal models and computer simulations are limited by the difficulty of capturing real life behaviour and preferences. To improve the effectiveness of our tool, we interviewed the key water users to derive their preference and replicate their behaviour in the simulation exercises. We found that our model replicates the current situation in the Piave River Basin well and were able to provide interesting and useful insights to water managers.

How negotiations work

For instance, we identified an important way that water management authorities could push water users towards cooperation. The authorities can threaten a “no agreement” water allocation rule that favours specific water users. Then, all water users will have an incentive to cooperate to avoid the imposition of the biased policy, but the resulting cooperative agreement will favour the preferred water users. A credible “no-agreement” policy is thus an important tool that the River Basin Authority can use to move parties towards a desired allocation rule.

When water users consider uncertain future water availability, they will all attempt to bargain to secure a higher water share to hedge against possible states of the world in which water is scarce. However, as an agreement is reached, only the stronger bargainers – those with greater political influence or smaller space for compromise – will be able to maintain advantage. In equilibrium, they will enjoy the benefits of their stronger bargaining stance at the expense of the weaker negotiators. Such agents are better off, ex post, than when following their deterministic strategies for a wide range of quantities of water available – that is, even when the situation is not one of extreme scarcity.

Thus, uncertainty increases the difficulty of reaching an equilibrium agreement. Their offers do not always converge, and in several occasions there is no allocation rule that satisfies all water users. This problem is exacerbated when users have different beliefs about the likelihood of a given quantity of water being available: in these cases, not only is an agreement more difficult to achieve, but the agents who believe that water will be more scarce bargain much harder to extract a larger share, causing weaker water users to bear even more risk.

Lessons from the model

Thus, there could be gains from investing to reduce uncertainty in water availability to all water users – perhaps through more targeted reservoir management or additional reservoirs to hedge against water flow fluctuations. Secondly, the value of information increases when disseminated evenly – that is, when all resource users have a common knowledge over water availability or its probability distribution, a self-enforcing agreement is easier to attain.

Our simulations indicate that proportional allocation rules are welfare improving compared to a fixed downstream allocation when water supply is uncertain. Furthermore, under proportional allocation, the risk of water shortage is spread evenly across users: this rule may be seen as fairer, reducing conflicts. Yet, a switch from fixed downstream to proportional allocation would necessarily cause the water users who benefit from the current system in the Piave River basin – namely the consumptive water users downstream – to incur losses to the benefit of currently weaker users. Loser may need compensation for change: for instance, irrigation infrastructure upgrades or additional water reservoirs in the lower part of the river to reduce vulnerability to water shortage.

In conclusion, exploring water management problems within a non-cooperative bargaining framework can help find politically and socially acceptable compromises. This exercise’s exploratory capacity may identify what aspects may be relevant in a negotiation, how a regulatory authority can influence negotiation outcomes, and other details of interest. Furthermore, this approach allows us to simulate the behaviour of water users under different rules, thus exploring the impacts of different policies on society, and how costs and benefits are distributed among individual users.


Adams, G., Rausser, G., and Simon, L. (1996), Modelling multilateral negotiations: an application to California Water Policy, Journal of Economic Behaviour and Organization, 30, 97-111.
Breslin, J. W., Dolin, E. J., and Susskind, L. F. (1992), International environmental treaty making, Harvard Law School, Cambridge, Massachusetts.
Breslin, J. W., Siskind, E., and Susskin, L. (1990), Nine case studies in international environmental negotiation, Harvard Law School, Cambridge, Massachusetts
Churchman, D. (1995), Negotiation: process, tactics, theory, University Press of America, Inc., Lanham, MD.
Conca, K., and Dabelko, G. D. (Eds.) (2002), Environmental Peacemaking, Woodrow Wilson Center Press, Washington D.C.
Dinar, A., and Alemu, S. (2000), The process of negotiation over international water disputes: the case of the Nile Basin, International Negotiations, 5, 331-356.
Rubinstein, A. (1982), Perfect Equilibrium in a Bargaining Model, Econometrica, 50, 97-110.
Sgobbi, A. and C. Carraro (2007), 'A Stochastic Multiple Players Multi-Issues Negotiation Model for the Piave River Basin', CEPR Discussion Paper 6585.
Simon, L., Goodhue, R., Rausser, G., Thoyer, S., Morardet, S., and Rio, P. (2006), 'Structure and power in multilateral negotiations: an application to French water policy', paper presented at 6th Meeting of Game Theory and Practice, Zaragoza, Spain, 10-12 July 2006.
Yoffe, S., Fiske, G., Giordano, M., Giordano, M., Larson, K., Stahl, K., and Wolf, A. T. (2004), Geography of international water conflict and cooperation: Data sets and applications, Water Resources Research, 40, 1-12.


1 Notable exceptions are the works of Adams et al. (1996) and Simon et al. (2006), who apply a bargaining model to analyse water management in California and Southern France respectively.




Topics:  Environment International trade

Tags:  water, shared resources

Professor of Environmental Economics and Econometrics, University of Venice and CEPR Research Fellow

Researcher, Fondatione Eni Enrico Mattei